Wyo. Stat. § 22-4-103: County central committee vacancies.

A vacancy in the county central committee shall occur in the case of death, resignation, failure of a qualified candidate to be elected to a precinct committeeman or committeewoman position, or removal of residence from the precinct. A vacancy shall be filled by the county central committee by election of a registered elector resident in the precinct in which the vacancy exists and registered in the party or as provided by the party bylaws.